Real Dictionary

resign
verb: If you resign from a job or position, you formally announce that you are leaving it.

resign in American English
to give up an office, position of employment, etc., esp. by formal notice
to give up possession of; relinquish (a claim, etc.)
intransitive verb: to give up an office or position, often formally
transitive verb: to give up (an office, position, etc.), often formally

resign in British English
verb: to give up tenure of (a job, office, etc)